I agree that you can exploit the structure of the Kircher Tree to make some interesting connections between various cards of the Major Arcana. This can be done with any version of the Tree of Life. But a few of the reasons I feel it's arbitrary are as follows.
First off, let's just look at the bottom-heavy structure of it. This serves a double purpose--it leaves room for the invisible eleventh Sephirah, Daath, and it shifts the emphasis of the Tree of Life downwards towards the more materialistic base (rather than the divine crown). This can represent the struggle of humanity to reconnect with the divine after the Fall, sure, but aren't there other ways to illustrate that relationship? The emphasis that Kircher places on the base of the Tree of Life reeks to me of a Calvinistic original-sin model of human nature. Compare it with
this top-heavy tree, which places more emphasis on the divine and sees the material world as a seed out of which divine knowledge grows. (It's more complicated than that, but you see the fundamental inversion in the way the tree approaches humanity and its relationship to the divine.) Or
this one, which presents the material and immaterial realms as equal and balanced. These differences in the way you frame any work with the Tree are, I think, fundamental influences on the outcome of that work, and that's why I'm suspicious of using only one.
Then let's talk about the way that cards are assigned to the Kircher tree. You just start at your top with the Fool and work your way down to the World at the bottom in numerical order, without any regard for the individual meanings of the cards, their astrological associations, or even the Kabbalistic meanings of the letters associated with them in texts like the
Sepher Yetzirah. And, well... Doesn't that feel a bit silly? Yes, with some of them, you get a meaningful placement--it makes sense for both the Emperor and the Hierophant to be on the masculine right side, connected to the Pillar of Mercy--but with other cases, it just seems so forced. The Moon on the masculine side of the Tree? And the Tower between Netzach and Hod?
Really? I understand that with enough work, you can probably derive something meaningful from looking at those correspondences, but there's also a certain point where you're trying to fit a square peg into a round hole, and I at least have asked myself numerous times if there wasn't a better way to do it.
Let's look back at the Lurianic tree (the first of the ones I've linked here). Rather than going from Aleph to Tau, this model splits the alephbet up into the Mother letters, the Single letters, and the Double letters, as outlined in the Sepher Yetzirah. It puts the three Mother letters on the three horizontal paths, the seven Doubles on the seven vertical paths, and the twelve Singles on the twelve diagonal paths. In my opinion, this presents a more consistent and coherent internal logic for the placement of the letters, at least, if not for the cards.
Now, of course, this model has its issues, too. The
Sepher Yetzirah provides a framework for the ordering of the Mothers, but with the Single letters, it once again starts at the top and just works its way down the alephbet (following the signs of the Zodiac as well). The same thing for the Double letters, which are assigned according to the Chaldean order of the planets--but then we have to ask ourselves whether we're using
Sepher Yetzirah or GD planetary correspondences. And, for example, the placement of the Hanged Man in the position formerly occupied by the Tower seems just as problematic to me. But I can at least follow and justify the placement with a bit more complexity of thought than just going from א to ת.
And if you look at the Lurianic or Gra trees here, you can still find useful thought-provoking structures. Death is still opposite Justice, but now the Devil is opposite Strength (a very interesting combination). And honestly, I think you could derive interesting material from the structural pairing of any two Major Arcana cards, so just because this
can be done with any one tree doesn't in any way make that tree complete or sufficient.
I agree that, as LRichard pointed out, the Tree of Life is just a two-dimensional glyph and is always going to be incomplete in some respects when it comes to representing the complexity of the universe and the human psyche. And furthermore, I acknowledge that all of these models are human devices and are going to be flawed to some extent because they're created by (flawed) people; I don't believe that there's any divine truth waiting to be distilled down into a single image. But I'm not really satisfied with resigning myself to that incompleteness, and to me, it seems that the best way to move past it is to work with multiple trees in conjunction in the hope that their respective flaws will balance each other out.
And finally (in a bit of a deviation, but while we're talking about associations with the Tree of Life and how I often feel they're arbitrary), I really can't get behind the magickal correspondences given for the Tree in
Liber 777. No reasoning is presented for them to be as they're given--no prior sources, no logical explanation for why things should be ordered a certain way. I admit I haven't read enough Judaic theology to know if there is, in fact, a grounding there for the angels and names of God as they're connected to the Tree in that book, but I feel that I can say with confidence that his correspondences for gems, plants, animals, and the like look like they came out of thin air (or perhaps an opium dream). I understand the argument that these correspondences are not necessarily external divine truths, but rather tools that can be used to focus a practitioner's mind during magickal work, but, well, I have trouble buying it. This is much less relevant to me, because, as I said, I don't practice magick, but it's definitely contributed to a larger sense of overall suspicion regarding Kabbalistic correspondences and the way they're presented and accepted as invariable (and, really, axiomatic) even though there's often not much explanation behind why things should be the way they're given.